Abstract Chemotaxis is a type of oriented movement of cells in response to the concentration gradient of chemical substances in their environment. We consider local existence and stability of nontrivial steady states of a logistic type of chemotaxis. We carry out the bifurcation theory to obtain the local existence of the steady state and apply the expansion method on the chemotaxis to investigate the bifurcation direction. Moreover, by applying the bifurcation direction, we obtain the bifurcating steady state is stable when the bifurcation curve turns to right under certain conditions.

Fund:This work is supported by the National Natural Science Foundation of China (No.11501031,11471221,71373023), Beijing Natural Science Foundation (1132003 and KZ201310028030) and Zhejiang A&F University telant program (2013FR078).

Chen-qing CAI,Qian XU,Xiao-lin LIU. The Local Bifurcation and Stability of Nontrivial Steady States of a Logistic Type of Chemotaxis[J]. Acta Mathematicae Applicatae Sinica, English Serie, 2017, 33(3): 799-808.